Alopecia areata (AA) is a CD8$^{+}$ T cell-dependent autoimmune disease that disrupts the constantly repeating cyclic transformations of hair follicles (HFs). Among the three main HF cycle stages-growth (anagen), regression (catagen) and relative quiescence (telogen)-only anagen HFs are attacked and thereby forced to prematurely enter into catagen, thus shortening active hair growth substantially. After having previously modelled the dynamics of immune system components critically involved in the disease development (Dobreva et al., 2015), we here present a mathematical model for AA which incorporates HF cycling and illustrates the anagen phase interruption in AA resulting from an inflammatory autoimmune response against HFs. The model couples a system describing the dynamics of autoreactive immune cells with equations modelling the hair cycle. We illustrate states of health, disease and treatment as well as transitions between them. In addition, we perform parameter sensitivity analysis to assess how different processes, such as proliferation, apoptosis and input from stem cells, impact anagen duration in healthy versus AA-affected HFs. The proposed model may help in evaluating the effectiveness of existing treatments and identifying new potential therapeutic targets.

中文翻译：

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分析斑秃作为毛囊循环的一种自身免疫性疾病的动力学模型。

斑秃（AA）是一种CD8 $ ^ {+} $ T细胞依赖性自身免疫疾病，可破坏毛囊（HF）不断重复的循环转化。在三个主要的HF循环阶段中，仅生长（生长期），回归（生长期）和相对静止（端源）的生长期HF受到攻击，从而被迫过早地进入生长期，从而大大缩短了活跃的头发生长。在先前对关键参与疾病发展的免疫系统成分的动力学进行建模之后（Dobreva et al。，2015），我们在此提出了一种结合了HF循环的AA的数学模型，并说明了由炎症性自身免疫引起的AA的生长期阶段中断对HF的反应。该模型将描述自身反应性免疫细胞动力学的系统与对毛发周期进行建模的方程式相结合。我们说明了健康，疾病和治疗的状态以及它们之间的过渡。另外，我们进行参数敏感性分析，以评估健康与受AA影响的HFs不同过程（如增殖，凋亡和干细胞输入）如何影响生长期。提出的模型可能有助于评估现有治疗的有效性并确定新的潜在治疗靶标。